• ON LIE RING OF GENERALIZED DERIVATIONS

Abstract

Let be the Lie ring of generalized derivations of a ring . In this article we show that the ring is a prime (semiprime) Lie ring if the ring is a prime (semiprime) of characteristic not equal to 2. Also we show that the Lie ring of generalized inner derivation is not a prime Lie ring for any ring . Further, examples are given to show that the conditions “characteristic not equal to 2" and “primeness" of the ring are not superfluous.